If 12a + 5b = 9, where a, b R, then minimum value of a^2 + b^2 is… - Vidyadip

MCQ

If $12a + 5b = 9$, where $a, b$ $\in$ $R$, then minimum value of $a^2 + b^2$ is -

A
$\frac{{31}}{9}$
B
$\frac{{169}}{81}$
✓
$\frac{{81}}{169}$
D
$\frac{{9}}{13}$

✓

Answer

Correct option: C.

$\frac{{81}}{169}$

c
$a=r \cos \theta $ and $ b=r \sin \theta$

$r=\frac{9}{(12 \cos \theta+5 \sin \theta)}$

minimum value of $\mathrm{r}=\frac{9}{13}$

$r^{2}=\frac{81}{169}$

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